ĐK: $x,y,z\geq 0$
$\sqrt{xyz}=(x+y)\sqrt{z}
\\\Leftrightarrow (x+y)\sqrt{z}-\sqrt{z}.\sqrt{xy}=0
\\\Leftrightarrow \sqrt{z}(x+y-\sqrt{xy})=0
\\\Leftrightarrow \left[\begin{matrix}\sqrt{z}=0\\ x+y-\sqrt{xy}=0\end{matrix}\right.
\\\Leftrightarrow \left[\begin{matrix}z=0\\ (\sqrt{x}-\dfrac{\sqrt{y}}2)^2+\dfrac{3y}4=0\end{matrix}\right.
\\\Leftrightarrow \left[\begin{matrix}z=0\\ x=y=0\end{matrix}\right.$
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